Here's a conundrum that I saw ages and ages ago. I know what the answer is, but I no longer remember the proof - maybe you can help?

As a follow-on to our last thought-provoking brain teaser, here's a poser that I first saw yonks and yonks ago when I was a bright-eyed young engineer.

Let's assume that we have two glasses of equal size. The two glasses contain different liquids, but they both contain the same quantity. Also, the liquid doesn't reach the top of the glasses, so if we wish there's room to add a teaspoon or two more liquid without them overflowing.

Now, let's assume that we remove a teaspoon's worth of liquid from Glass A, add it to the contents of Glass B, and then vigorously stir the contents of Glass B (assume that – unlike oil and vinegar – these two fluids will happily mix together).

Finally, let's assume that we remove a teaspoon's worth of the new mixture from Glass B, add it to the contents of Glass A, and vigorously stir the contents of Glass A.

So, we've returned to having the same amount of liquid in both glasses. The question is ... is the mixture in Glass A (the proportion of Fluid A to Fluid B) more concentrated than the mixture in Glass B (the proportion of Fluid B to Fluid A) – or is the mixture in Glass A less concentrated than the mixture in Glass B – or are the two concentrations the same?

As I say, I remember what the answer is (no, I'm not going to tell you), but I can no longer recall the mathematical proof and this is really starting to "niggle" me. Can you help?

No math. Since we don't know the spoon size, we can assume it's equal to the quantity of a liquid in a glass (of coarse a glass should take this additioal amount).
Now put both into one glass, mix and take half back. Here we are - concentration is equal.
Gennady